🧮 algebra

1. **State the problem:** Solve for $j$ in the equation $$\frac{5}{8} j + \frac{3}{4} = \frac{1}{2}$$. 2. **Isolate the term with $j$:** Subtract $\frac{3}{4}$ from both sides:

1. **State the problem:** Solve the two-step equation $$\frac{3}{7}(a - 6) = -2$$ for $$a$$. 2. **Understand the formula and rules:** To solve for $$a$$, first eliminate the fracti

1. **State the problem:** Solve the two-step equation $$-4 = \frac{8}{9} (u - 3)$$ for $u$. 2. **Isolate the term with $u$:** To get rid of the fraction $$\frac{8}{9}$$, multiply b

1. **State the problem:** Solve for $d$ in the equation $$\frac{1}{2} d + \frac{2}{3} = \frac{3}{4}$$. 2. **Isolate the term with $d$:** Subtract $\frac{2}{3}$ from both sides:

1. **State the problem:** Solve the equation $$\frac{2}{5}\left(j + \frac{7}{2}\right) = 5$$ for $j$. 2. **Identify the formula and rules:** This is a two-step equation involving f

1. **State the problem:** Solve for $n$ in the equation $$-\frac{3}{5} (n - \frac{1}{2}) = 1$$. 2. **Isolate the parenthesis:** To eliminate the fraction coefficient, divide both s

1. **State the problem:** Solve the inequality $$4(2x + 1) < 4$$ and graph the solution on a number line. 2. **Use the distributive property:** Multiply $$4$$ by each term inside t

1. **State the problem:** Solve the inequality $$-6(7 - 3x) > 12$$ and graph the solution. 2. **Apply the distributive property:** Multiply $$-6$$ by each term inside the parenthes

1. **State the problem:** We are given that 20 Australian dollars (AUD) equals 540 South African rands (ZAR). We need to: (i) Draw a conversion graph between AUD and ZAR.

1. **State the problem:** Aria wants to decide between two parking garages. Garage A charges $7 plus $3 per hour, and Garage B charges $4 plus $4 per hour. We want to write equatio

1. **State the problem:** We want to compare how many miles Serenity and Julia can each drive on one gallon of gas. 2. **Serenity's mileage:** Given by the equation $$y = 35.2x$$,

1. **State the problem:** A girl of height $90$ cm (which is $0.9$ m) walks away from a lamp-post that is $3.6$ m tall at a speed of $1.2$ m/s. We want to find the length of her sh

1. **State the problem:** We need to solve the simultaneous linear equations: $$4a + 3b = -6$$

# Exercice 6 1. Montrer que : $\forall x \in \mathbb{R} \setminus \left\{\frac{2}{3}\right\} : \frac{4x+1}{3x-2} \neq \frac{4}{3}$

1. Énoncé du problème : Vérifier si l'égalité $\sqrt{x+1} = 1 + \frac{x}{2}$ est vraie pour $x \neq 0$.

1. The user asked to redo part b of a problem, but the original problem context is missing. 2. Please provide the full problem or part b details so I can assist accurately.

1. Montrons que $(y \neq 2 \text{ et } y \neq -2) \Rightarrow (2y^2 - 8 \neq 0)$.\n\n2. Montrons que $(x \neq 0) \Rightarrow (\sqrt{x} + 1 \neq 1 + \frac{x}{2})$.\n\n3. Montrons qu

1. **State the problem:** We want to find a formula for the sum

1. **State the problem:** We have a base sequence with nth term $n^2$: 1, 4, 9, 16, ... 2. **Given sequences:**

1. **State the problem:** Robyn converted some amount of money in pounds (£) to euros (€) at one of two airports. She received €68.31. We want to find the smallest amount of pounds

1. **State the problem:** Robyn received €68.31 after converting pounds at one of two airports with different exchange rates. We need to find the smallest amount of pounds she coul